Fleming was born in Glasgow where he attended the School of Art, 1924-9. Chika Macnab and Charles Murray were his initial printmaking teachers, then he worked with Robert Sargent Austin and Malcolm Osborne for several months of a travelling scholarship at Royal College of Art, additional studies being made in France and Spain. Fleming taught at Glasgow School of Art, 1931-48, at Hospitalfield from 1948-54, then he was principal of Gray's School of Art, Aberdeen, 1954-72, where he developed printmaking.

Fleming scored an early success in 1931 when he engraved Gethsemane, bought by the French government and also in the collection of Scottish National Gallery of Modem Art. His later work was notable for experiment both in printmaking and in watercolour. Glasgow School of Art holds Fleming's fine picture The Painters Robert Colquhoun and Robert MacBryde, who were his pupils.